Question

A 72.8-kg swimmer is standing on a stationary 265-kg floating raft. The swimmer then runs off the raft horizontally with a velocity of 5.21 m/s relative to the shore. Find the recoil velocity that the raft would have (again relative to the shore) if there were no friction and resistance due to the water.

Answer 1

-1.43 m/s relative to the shore

Step-by-step explanation:

Total momentum must be conserved before and after the run. Since they were both stationary before, their total speed, and momentum, is 0, so is the total momentum after the run off:

`m_sv_s + m_rv_r = 0`

where
`m_s = 72.8, m_r = 265` are the mass of the swimmer and raft, respectively.
`v_s = 5.21 m/s, v_r` are the velocities of the swimmer and the raft after the run, respectively. We can solve for
`v_r`

`265v_r + 72.8*5.21 = 0`

`v_b = -72.8*5.21/265 = -1.43 m/s`

So the recoil velocity that the raft would have is -1.43 m/s after the swimmer runs off, relative to the shore